If you search the census, there are a few of that name living in the Falls Ward of Belfast.
Put in "Dillon", "Antrim" (County), and "Falls" (DED)
There are't so many in the 1901 census as the 1911.
There are a few wills on the PRONI sit that might help too.
I had a quick look and one is for Annie Dillon of Lower Clonard Street (Falls Road area).www.census.nationalarchives.iewww.proni.gov.uk